The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 X^2 1 1 X^3 1 1 1 1 X^2 1 1 1 0 X^3+X^2 0 X^3+X^2 0 X^3+X^2 0 X^2 X^3 X^3+X^2 0 X^3+X^2 X^3+X^2 0 X^3 X^2 X^3 X^2 X^2 X^3 0 0 X^3+X^2 X^3+X^2 0 X^3+X^2 X^3+X^2 0 X^3+X^2 0 X^3 X^2 X^3 X^3+X^2 0 X^2 X^3+X^2 X^3+X^2 0 0 X^2 X^3 X^2 X^3 X^3 X^2 X^3 X^3+X^2 0 X^3+X^2 0 X^3 X^2 0 X^3+X^2 0 X^3+X^2 X^2 X^3+X^2 X^3 0 X^3 X^3 0 X^3 X^3+X^2 X^2 X^3 0 0 0 0 0 X^3 0 0 0 0 0 X^3 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 0 0 0 X^3 0 0 X^3 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 0 0 X^3 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 0 X^3 0 0 0 0 0 0 0 X^3 0 0 0 X^3 0 0 0 X^3 0 0 0 X^3 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 0 0 0 0 0 0 X^3 0 0 0 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 0 0 X^3 0 X^3 0 0 X^3 0 X^3 X^3 0 0 0 0 0 0 0 0 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 0 0 0 0 0 0 0 0 X^3 0 X^3 X^3 0 0 0 0 X^3 0 0 0 0 0 0 0 0 0 0 X^3 0 X^3 0 X^3 0 0 0 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 0 X^3 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 0 0 X^3 X^3 0 0 0 generates a code of length 71 over Z2[X]/(X^4) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+63x^64+120x^67+32x^68+256x^69+567x^70+64x^71+536x^72+256x^73+32x^74+48x^75+24x^78+8x^80+24x^83+16x^86+1x^134 The gray image is a linear code over GF(2) with n=568, k=11 and d=256. This code was found by Heurico 1.16 in 0.469 seconds.